• Journal of KSNVE
• /
• v.8 no.2
• /
• pp.353-360
• /
• 1998

In this paper, a modeling method for the bending vibration analysis of rotating Timoshenko beams with concentrated mass and mass moment of inertia is presented. The shear and rotary inertia effects become critical for the accurate estimation of the natural frequencies and mode shapes as the slenderness ratio decreases. The natural frequencies obtained by using the Timoshenko beam theory are lower than those by using the Euler beam theory. The critical angular speed, which does not exist only with the concentrated mass, exists with the concentrated mass moment of inertia.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.13 no.1
• /
• pp.63-69
• /
• 2003

The ordinary differential equations governing free vibrations of elastic horizontally curved beams are derived, in which the effects of rotatory inertia and shear deformation as well as the effects of both vertical and torsional inertias are included. Frequencies and mode shapes are computed numerically for parabolic curved beams with the hinged-hinged, hinged-clamped and clamped-clamped ends. Comparisons of natural frequencies between this study and ADINA are made to validate the theories and numerical methods developed herein. The lowest three natural frequency parameters are reported. with and without the effects of rotatory inertia and shear deformation. as functions of the three non-dimensional system parameters: the horizontal rise to span length ratio. the slenderness ratio and the stiffness parameter.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1997.10a
• /
• pp.110-115
• /
• 1997

A modeling method for the bending vibration analysis of rotating Timoshenko beams with concentrated mass and mass moment of inertia is presented. The shear and rotary inertia effects become critical for the accurate estimation of the natural frequencies and modeshapes as the slenderness ratio decreases. The effect of the concentrated mass and mass moment of inertia on the natural frequencies are also investigated with the modeling method.

• Journal of the Korea Concrete Institute
• /
• v.12 no.2
• /
• pp.71-78
• /
• 2000

This paper presents a study on the flexural rigidity of reinforced high strength concrete beams. Thirty six beams with different compressive strength of concrete, tensile reinforcement ratio, compressive reinforcement ratio, and pattern of loadings(1 point loading and 2 points loading) were tested to evaluate the effective moment of inertia. According to the experimental results, the eqation(1) proposed by ACI code for the effective moment of inertia overestimated that of simply supported reinforced high strength concrete beams. Thus, in this paper, an empirical equation(3) is proposed as a lower bound of 90% confidence limit to estimate the effective moment of inertia of simply supported reinforced high strength concrete beams.

• Structural Engineering and Mechanics
• /
• v.38 no.4
• /
• pp.459-477
• /
• 2011

Due to the low elastic modulus of FRP, concrete members reinforced with FRP rebars show greater deflections than members reinforced with steel rebars. Deflection is one of the important factors to consider the serviceability of horizontal members. In this study flexural test of AFRP reinforced concrete beams was performed considering reinforcement ratio and compressive strength as parameters. The test results indicated that flexural capacity and stiffness increase in proportion to the reinforcement ratio. The test results were compared with existing proposed equations for the effective moment of inertia including ACI 440. The most of the proposed equations were found to over-estimate the effective moment of inertia while the equation proposed by Bischoff and Scanlon (2007) most accurately predicted the values obtained through actual testing.

• Journal of KSNVE
• /
• v.6 no.2
• /
• pp.179-185
• /
• 1996

This paper presents a modeling method for the vibration analysis of a rotating beam the slenderness ratio of which is relatively small. The smaller the slenderness ratio becomes, the larger the shear and rotary inertia effects become. Such effects become critical for the accurate estimation of the natural frequencies and modeshapes, especially higher frequencies and modes, as the angular speed increases. It is also shown that the effects are important for the accurate estimation of the critical angular speed of the beam.

• Structural Engineering and Mechanics
• /
• v.3 no.5
• /
• pp.511-525
• /
• 1995

The differential equations governing in-plane free vibrations of the elastic, catenary arch with rotatory inertia are derived in Cartesian coordinates. Frequencies and mode shapes are computed numerically for such arches with unsymmetric axes, for both clamped-clamped and hinged-hinged end constraints. The lowest four natural frequency parameters are reported, with and without rotatory inertia, as a function of three nondimensional system parameters; the span to cord length ratio e, the slenderness ratio s, and the rise to cord length ratio f. Experimental measures of frequencies and mode shapes for several laboratory-scale catenary models serve to validate the theoretical results.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2002.10a
• /
• pp.11-16
• /
• 2002

The differential equations governing free vibrations of the elastic, horizontally curved beams with unsymmetric axis are derived in Cartesian coordinates rather than in polar coordinates, in which the effect of torsional inertia is included. Frequencies are computed numerically for the sinusoidal curved beams with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported, with and without torsional inertia, as functions of three non-dimensional system parameters: the horizontal rise to chord length ratio, the span length to chord length ratio, and the slenderness ratio.

• Journal of the Korea Concrete Institute
• /
• v.20 no.3
• /
• pp.393-404
• /
• 2008

The approaches in many design codes for the estimation of the deflection of flexural reinforced concrete (RC) members utilize the concept of the effective moment of inertia which considers the reduction of flexural rigidity of RC beams after cracking. However, the effective moment of inertia in design codes are primarily based on the ratio of maximum moment and cracking moment of beam subjected to loading without proper consideration on many other possible influencing factors such as span length, member end condition, sectional size, loading geometry, materials, sectional properties, amount of cracks and its distribution, and etc. In this study, therefore, an experimental investigation was conducted to provide fundamental test data on the effective moment of inertia of RC beams for the evaluation of flexural deflection, and to develop a modified method on the estimation of the effective moment of inertia based on test results. 14 specimens were fabricated with the primary test parameters of concrete strength, cover thickness, reinforcement ratio, and bar diameters, and the effective moments of inertia obtained from the test results were compared with those by design codes, existing equations, and the modified equation proposed in this study. The proposed method considered the effect of the length of cracking region, reinforcement ratio, and the effective concrete area per bar on the effective moment of inertia, which estimated the effective moment of inertia more close to the test results compared to other approaches.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.7 no.2
• /
• pp.3-18
• /
• 1970

An investigation was made for the added mass moment of inertia induced by the rotational motion of the cylinder with hull section on water in order to obtain the information to estimate the natural frequency of the torsional vibration of ships. The special consideration to the effect of the draught upon the added mass moment of inertia is taken into account in the study. In this paper, the general expression for the added mass coefficients of moment of inertia of arbitary two dimensional forms induced by the torsional vibration, was derived by the author. Hence, the coefficients for these forms are represented as functions of parameters, the section area coefficient and draft beam ratio, from which the added mass coefficients for arbitrary forms can be obtained. The result was shown in a chart for estimation of the added mass moment of inertia induced by the torsional vibration, as first trial, for the convenience of practical use.